Fofana gave his side a fourth minute lead with a superb shot from the edge of the box before Krasso made up for an earlier miss when he acrobatically netted a second just before the hour.
The Ivorians were always favorites against a Guinea Bissau team who have now not won any of their 10 Cup of Nations finals matches but the hosts, with several players missing through injury, will be pleased to have started their campaign on a positive note in front of an expectant 60,000 crowd.
Twice winners Ivory Coast next play on Thursday when they face Nigeria in the biggest match-up in the group, while Guinea-Bissau take on Equatorial Guinea on the same day. The games will again be played at Abidjan's Alassane Ouattara Stadium.
It was a far from perfect performance from the hosts and Guinea Bissau were left to rue several missed opportunities, but Ivory Coast coach Jean-Louis Gasset will know the three points are all that matters at this early stage of the tournament.
The Frenchman's side got a dream start when Fofana curled his shot into the top corner from 20 meters, settling the nerves of the home players and their supporters.
But after the Ivorians' fast start, Guinea Bissau settled into the contest and created a few chances themselves.
Forward Mama Balde went for a spectacular bicycle kick when he might have opted for a header before he had an excellent chance to equalize with a clear run on goal but his shot was weak and easily saved by Yahia Fofana.
Seko Fofana came close to a second goal when his powerful drive from the edge of the box was tipped onto the crossbar by Guinea-Bissau's Ouparine Djoco, who was a surprise selection over regular goalkeeper Jonas Mendes.
The hosts created another superb opening before the break when Jonathan Bamba fed Krasso in the box only for the striker to turn the ball wide.
Guinea-Bissau started the second half on the front foot but too often their final pass was poor and they wasted promising positions.
The home side doubled their advantage after 58 minutes when Krasso profited from some hesitant defending and took two touches before acrobatically rifling the ball into the net.
Guinea-Bissau had half-chances after that but have now stretched their run of games without a goal at the Cup of Nations finals to eight.
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